带位势项的半线性波动方程解的生命跨度的上界估计

Upper Bound Estimate of Lifespan of Solutions for Cauchy Problem for Semilinear Wave Equations with Potential

拟在n(n≥3)维空间中研究带有次临界指数的非线性项与位势项的半线性波动方程。通过采用试探函数方法,证明了小初值Cauchy问题的解总会在有限时间内破裂,并得到带位势项的半线性波动方程在次临界情形时解的破裂性态,从而建立问题解的生命跨度的上界估计。

This paper is concered with the semilinear wave equation with the critical exopontional nonlinear term and potential items in the dimension n(n≥3).By constructing a test function,the blowup behavior of solutions to the Cauchy problem with small initial data is established.We prove that solutions always blow-up in finite time.The blow-up criterion of solutions to the problem in the subcritical case with a potential is obtained.We investigate the upper bound life span of solutions to the problem.